Polar motion excitations for an Earth model with frequency-dependent responses: 1. A refined theory with insight into the Earth's rheology and core-mantle coupling

This study aims to improve the polar motion theory by developing refined frequency-dependent transfer functions with the most current models for ocean tides, the Earth's rheology, and core-mantle coupling. First, we present a power law for mantle anelasticity constrained by the Chandler period T-CW and quality factor Q(CW) and an empirical quasi-fluid rheology model with a linear dependence on frequency, which is suitable for a period as long as similar to 18.6 years. Then we adopt the diurnal ocean tides from the International Earth Rotation and Reference Systems Service Conventions (2010), the long-period ocean model of Dickman and Gross (2010), and the equilibrium ocean pole tide model of Desai (2002) to calculate the oceanic corrections to the Love numbers. Further, we present discussions on the geophysical and observational aspects of the Chandler period TCW and quality factor Q(CW), and provide preferred values and intervals for T-CW and Q(CW), which allow us to place some constraints on the mantle anelasticity and core-mantle coupling ratio (CW). Although (CW) is affected by uncertainties in T-CW and Q(CW), we find its real part should be around 2%-3% while its imaginary part might be only a few thousandths. Finally, the frequency-dependent polar motion transfer functions T-L and T-NL are determined based on the models of frequency-dependent Love numbers and core-mantle coupling discussed above. Our transfer functions are related to the values of T-CW and Q(CW), however, our analyses demonstrate that our transfer functions are rather stable and not sensitive to perturbations in T-CW and Q(CW)